Bright-Dark Solitons, Kink Wave and Singular Periodic Wave Solutions for the Lonngren-Wave Equation

Abstract

In this article, exact solutions of the Lonngren-wave equation are investigated. Firstly, the equation is transformed into an ordinary differential equation by traveling wave transformation. Based on the homogeneous balance method, bright-solitons and singular periodic wave solutions of the equation are derived by applying the simple function expansion method and the Riccati equation method. Applying the $Exp(−φ(ς))$ expansion method, we construct dark-solitons and kink wave solutions of the equation. Moreover, the 3-D, 2-D and density plots are drawn by choosing the appropriate parameters so that the properties of the solutions can be better studied. According to the Figures, the analysis of the dynamical behavior of the solutions is provided. This article enriches the diversity of the solutions of the equation.